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2 years ago

14

Why do you think a removable discontinuity (hole) doesn't produce an asymptote on the graph of a polynomial function, even thoug

h it is excluded from the domain of the function?

1 answer:

Monica [59]2 years ago

8 0

Because removable discontituity means that the limit of the function at that point has a finite value, and then you define the value of the function as that valu (the limit value).

An asymptote means that the limit of the function goes to positive or negative infinity.

You cannot meet both conditions, finite and infinity limit at the same time.

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4. Suppose that Peculiar Purples and Outrageous Oranges are two different and unusual types of bacteria. Both types multiply thr

Viktor [21]

Answer:

Peculiar purples would be more abundant

Step-by-step explanation:

Given that eculiar Purples and Outrageous Oranges are two different and unusual types of bacteria. Both types multiply through a mechanism in which each single bacterial cell splits into four. Time taken for one split is 12 m for I one and 10 minutes for 2nd

The function representing would be

i) $P=P_0 (4)^{t/12}$ for I bacteria where t is no of minutes from start.

ii) $P=P_0 (4)^{t/10}$ for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.

a) Here P0 =3, time t = 60 minutes.

i) I bacteria P = $3(4)^{5} =3072$

ii) II bacteria P = $3(4)^{4} =768$

b) Since II is multiplying more we find that I type will be more abundant.

The difference in two hours would be

$3(4)^{10}- 3(4)^{8} =2949120$

c) i) $P=P_0 (4)^{t/12}$ for I bacteria where t is no of minutes from start.

ii) $P=P_0 (4)^{t/10}$ for II bacteria where t is no of minutes from start. P0 is the initial count of bacteria.

d) At time 36 minutes we have t = 36

Peculiar purples would be

$i) P=3 (4)^{36/12}=192$

The rate may not be constant for a longer time. Hence this may not be accurate.

e) when splits into 2, we get

$P=P_o (2^t)$ where P0 is initial and t = interval of time

7 0

2 years ago

Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference fo

MAVERICK [17]

Answer:

a

The Null hypothesis represented as

$H_0: \mu_1 - \mu_2 = 0$

The Alternative hypothesis represented as

$H_a: \mu_1 - \mu_2 < 0$

b

p-value = P(Z < -3.37 ) = 0.000376

c

There is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

Step-by-step explanation:

From the question we are told that

The population size is $n= 650$

The sample size for graduates is $n_1 = 300$

The sample mean for graduates is $\= x _1 = 148$

The sample standard deviation for graduates is $\sigma_1 = 16$

The sample size for under-graduates is $n _2 = 350$

The sample mean for under-graduates is $\= x _2 = 153$

The sample standard deviation for graduates is $\sigma_2 = 21$

The Null hypothesis represented as

$H_0: \mu_1 - \mu_2 = 0$

The Alternative hypothesis represented as

$H_a: \mu_1 - \mu_2 < 0$

Where $\mu_1 \ and \ \mu_2$ are the population mean

Now the test statistic is mathematically represented as

$t = \frac{(\= x_1 - \= x_2 ) }{ \sqrt{ \frac{ (n_1 - 1 )\sigma_1 ^2 + (n_2 - 1)\sigma_2^2}{n_1 +n_2 -2} } * \sqrt{ \frac{1}{n_1} + \frac{1}{n_2} } }$

substituting values

$t = \frac{(148 - 153 ) }{ \sqrt{ \frac{ (300- 1 )16 ^2 + (350 - 1) 21^2}{300 +350 -2} } * \sqrt{ \frac{1}{300} + \frac{1}{350} } }$

$t = -3.37$

The p-values is mathematically evaluated as

p-value = P(Z < -3.37 ) = 0.000376

The above answer is gotten using a p-value calculator at (0.05) level of significance

Looking the p-value we see that it is less than the level of significance (0.05) so Null hypothesis is rejected

Hence there is insufficient evidence to conclude that graduate students score higher, on average, on the HPI than undergraduate students

6 0

2 years ago

For the sequence an = 2n + 1, identify the values of a0 = _____, a1 = _____, a2 = _____, and a3 = _____.

Tresset [83]

Answer:

Option A - $a_0= 2,a_1= 3,a_2= 5,a_3= 9$

Step-by-step explanation:

Given : For the sequence $a_n= 2^n + 1$

To find : Identify the values of following?

Solution :

The nth term of the sequence is $a_n= 2^n + 1$

Substitute n=0,1,2 and 3

When n=0,

$a_0= 2^0+ 1$

$a_0= 1+1$

$a_0=2$

When n=1,

$a_1= 2^1+ 1$

$a_1= 2+1$

$a_1=3$

When n=2,

$a_2= 2^2+ 1$

$a_2=4+1$

$a_2=5$

When n=3,

$a_3= 2^3+ 1$

$a_3= 8+ 1$

$a_3= 9$

Therefore, The value is $a_0= 2,a_1= 3,a_2= 5,a_3= 9$

So, Option A is correct.

4 0

2 years ago

Given the equation, y=3x – 7 what is the slope of the line?

Natasha_Volkova [10]

<span>y=3x – 7
slope = 3

hope it helps</span>

4 0

2 years ago

Read 2 more answers

Sara lit a new candle and then recorded its height in inches every hour as (time, height). Her results were Syntax error.

Keith_Richards [23]

Answer: A

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers